Twitter Plugin Settings
A number of users have reported problems with displaying Twitter feeds on their blog. There have been some changes to how Twitter allows use of its APIs. This means that your blog / WordPress plugins will probably need to be authorised to use your Twitter feeds.
You should start by visiting the settings page for your Twitter plugin. The screenshot below shows the settings for Twitter Widget Pro:
Enter the name of your blog, a description and your blog web address for both Website and Callback URL. Complete the captcha code and you should be presented with your consumer tokens/keys. Use these keys and secrets on your WordPress plugin as shown below and your Twitter feeds should start working again.